Avigdor Lieberman, left, with Binyamin Netanyahu. The rise of Moldovan-born Lieberman is attributed to solid support among the Russian-speaking community. Photograph: Jim Hollander/EPA

At a large supermarket in the coastal city of Ashdod, where more than 50 brands of vodka are available alongside pork chops, bacon, sausages and ham, Arthur Rosen, who came to Israel from Ukraine as a teenager, reflects on the drawbacks of democracy.

"The problem with Netanyahu is that he doesn't have enough power. [Israel] is a democracy, which means everyone says what they want," he says, specifically citing two Israeli-Arab members of parliament, Haneen Zoabi and Ahmed Tibi. "Everyone speaks, and that's not good. I prefer the Russian system where Putin has much more power."

Rosen, 34, is one of more than a million citizens of Israel who emigrated from Russia, Ukraine and other countries following the collapse of the Soviet Union more than two decades ago. Comprising about 15% of eligible voters, Israel's Russian-speaking community is a powerful constituency in next week's general election.

Like many of those who came to Israel as youngsters, Rosen identifies himself as Israeli. "I've spent half my life here, and my children were born here." He plans to vote for the electoral alliance between the rightwing parties of Binyamin Netanyahu and Avigdor Lieberman, known as Likud-Beiteinu, citing "strength" as the defining factor.

His views are echoed by Abigail Kold, 31, who came from Russia 13 years ago. "I was a child under communism. People were afraid of the government," she says. The Israeli left is more socialist than communist "but it's all utopia. They don't know what they're talking about." She, too, intends to vote for Likud-Beiteinu.

Many new immigrants from the former Soviet Union settled in Russian-speaking enclaves, where the language, food and culture were familiar. The city of Ashdod doubled in size in a decade.

Some found themselves marginalised in the early days, consigned to low-paid and low-status jobs, and with doubts cast over their Jewishness. Israel granted citizenship to anyone from the former Soviet Union with a Jewish parent or grandparent, or who was married to someone meeting that criteria, rather than the strict matrilineal descent required by Jewish orthodox law.

According to Israel's central bureau of statistics, about 30% of immigrants from the former Soviet Union in the 1990s were not considered Jewish under orthodox law, a figure that rose to 59% in 2005. Only a small proportion have formally converted to Judaism.

But their impact on Israeli politics has been marked. The rise of Lieberman, the ultra-nationalist former foreign minister, himself an immigrant from Moldova, is attributed to solid support among the Russian-speaking community for his uncompromising rightwing agenda: opposing concessions to the Palestinians, supporting settlements and seeking to curb the rights of Israel's Arab population.

According to Ze'ev Khanin, a political scientist at Bar-Ilan and Ariel universities, the "Russian vote" accounts for about 20 of the 120 seats in the Knesset. Conservative estimates suggest 50%-60% will vote for Likud-Beiteinu on Tuesday, he says.

But, he adds, they are more integrated than ever before. "The Russian-speaking community is identifiable, but it is part of the Israeli collective. The second generation is much more influenced by its Israeli experience than its Soviet past." They are less interested in political parties devoted to "Russian issues" and more attracted to mainstream, albeit rightwing, parties.

Vladimir Dzyakevich, who came to Israel from Moscow at the age of 10, says many in the community are shaped both by their Russian heritage and their present lives as Israelis. "Their ideology is shaped there, but their sense of reality is shaped here."

Now 32, the part-time biologist and part-time actor in Ashdod's Russian Theatre says the Russian-speaking community tends to be attracted to strong leaders. In times of uncertainty, "you look for someone who will bring order. Democracy is a costly way to run a country – sometimes you have to stop talking and just do things".

Dzyakevich, who has always voted for a mainstream party in the past, this time plans to back the tiny Eretz Hadasha, an anti-corruption party. "Israel has become a place where rich people rule. Almost every politician is supported by a rich guy. We have to break it up."

Some in the community "are culturally really Russian and live in a ghetto. Others forget they are Russian. I'm somewhere in the middle – I don't forget my heritage, but I feel part of this country."

Just as in any community, he says, there is a spectrum of political opinion, and he is at the liberal end of it. "Russians don't vote like goats," he adds with a smile.